An image either is, or can be transformed into, an ordered set of pixels. Each pixel has a location in the image, i.e., relative to all other pixels in the set, and one or more values defining the pixel's intensity and color. In the case of MRI images, there is typically only one value for a pixel, and that is the pixel's intensity.
In MRI images of the brain, there are three tissue types of particular interest, namely white matter (“WM”), gray matter (“GM”), and cerebrospinal fluid (“CSF”). Setting aside the skull, the remaining three of these tissue types are distinguished in the image by their intensities: Pixels representing WM have a relatively high intensity; pixels representing GM have a relatively moderate intensity; and pixels representing CSF have a relatively low intensity.
A fundamental problem in the interpretation of images generally is that of associating pixels having similar values, to identify particular objects. In the MRI image for example, it is desired to classify a given pixel, based on its intensity alone, as representing either WM, GM, or CSF. In the aggregate, this allows the identification of structures.
It may be noted at this point that the term “pixel” refers to a quantum area and assumes a two-dimensional image. If the image is three-dimensional, the corresponding quantum volume is termed a “voxel.” In the context of image segmentation, the same principles apply.
One simple type of image segmentation, referred to as “thresholding,” defines a range within which the absolute pixel value can be considered to represent a given structure type. So, for example, a range of intensities (normalized between 0 and 1.0) for a pixel to be considered WM may be 0.7-1.0; a range for GM may be 0.4-0.69; and a range for CSF may be any value less than 0.39.
A well known problem with thresholding results from the fact that there are always intensity inhomegeneities (“IIH”) within the image. These are necessarily spatial, but may be random or not. As a result, a first pixel representative of WM at a first location in the image may have an intensity of 0.75, whereas a second pixel representative of the same tissue type at a second location in the image may have an intensity of only 0.65. Under the thresholding scheme described above, the WM would be correctly classified at the first location, but would be incorrectly classified as GM at the second location.
There are numerous strategies for addressing this problem, two general categories of which are noteworthy for purposes herein. One of these seeks to correct for the IIH. This may be done as a pre-processing step or simultaneously with the segmentation process. The other general category of strategies for addressing the problem of IIH is known as “deformable modeling,” which seeks to define the boundaries between different structures, which are more robust to IIH than are individual pixels.
All of these strategies have at least one major drawback in common, which is that they conduct optimizations (i.e., of an objective function) that, while finding local optima, do not ensure the finding of global optima. There are also a number of other disadvantages, specific to the strategies generally, and specific to particular examples thereof, that are known to persons of ordinary skill in the art. It will be readily appreciated by such persons that a new strategy is needed that is both robust to IIH and does not have this “local versus global” optimization problem.